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Maximal and Principal Ideals

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Let delta=sqrt(-3) and R=Z[delta]. This is not the ring of integers in the imaginary quadratic number field Q[delta]. Let A be the ideal (2,1+delta).
a) Show that A is a maximal ideal and identify the quotient ring R/A.
b) Show that A contains the principal ideal (2) but that A does not divide (2).

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In this solution, we provide proof that A is a maximal ideal, and contains the principle ideal but does not divide.

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